Understanding Function Shifts

The video tutorial explains how to express one function, G(x), in terms of another function, F(x), by applying horizontal and vertical shifts. It begins with an introduction to two similar graphs and the task of expressing G in terms of F. The tutorial then delves into the concept of shifting functions, explaining how to align F with G through horizontal and vertical shifts. It provides a detailed example using a specific function to demonstrate the process of expressing G in terms of X, highlighting the importance of understanding shifts in function transformations.

What is the main task when comparing the graphs of F(x) and G(x)?

• Determining the area under the curves

• Calculating the slope of the tangent

• Writing a formula for G(x) in terms of F(x)

• Finding the intersection points

How do you express a horizontal shift to the left in a function?

• Add a positive number to x

• Multiply x by a negative number

• Divide x by a positive number

• Subtract a positive number from x

What is the vertical shift when moving from y = 2 to y = -5?

• Shift up by 7

• Shift down by 7

• Shift up by 3

• Shift down by 3

Why does a left shift in the function result in a positive addition to x?

• To increase the function's range

• To maintain the same output value

• To decrease the function's domain

• To simplify the function

What is the horizontal shift when moving two units to the left?

• Add 2 to x

• Subtract 2 from x

• Divide x by 2

• Multiply x by 2

In the new example, what is the vertical shift from y = -2 to y = 3?

• Shift down by 5

• Shift up by 5

• Shift down by 3

• Shift up by 3

How do you express G(x) in terms of F(x) when given a horizontal shift of -2?

• F(x) + 2

• F(x + 2)

• F(x) - 2

• F(x - 2)

What is the final expression for G(x) when F(x) is defined as the square root of (x + 4) - 2?

• Square root of (x + 6) + 3

• Square root of (x + 6) - 2

• Square root of (x + 2) + 5

• Square root of (x + 2) - 5

What is the purpose of substituting x + 2 for x in the function F(x)?

• To express G(x) in terms of x

• To calculate the integral

• To determine the function's maximum

• To find the derivative

What is the result of adding 5 to the expression for F(x + 2)?

• It stretches the graph vertically

• It shifts the graph up by 5

• It shifts the graph down by 5

• It compresses the graph horizontally